The CGFFT method with a discontinuous FFT algorithm

TLDR: In this article, an efficient FFT algorithm is developed for discontinuous functions with both uniform and non-uniform sampled data, with O(Np+N log n) complexity, where N is the number of sampling points and p is the interpolation order.

Abstract: In the conjugate gradient–fast Fourier transform (CGFFT) method, the FFT is used to evaluate the convolution integrals. When the function to be transformed has discontinuities, the accuracy of the FFT results, and thus the CGFFT results, will degrade. In this letter, an efficient FFT algorithm is developed for discontinuous functions with both uniform and nonuniform sampled data, with O(Np+N log N) complexity, where N is the number of sampling points and p is the interpolation order. The algorithm is incorporated into the CGFFT method. Numerical results for slabs demonstrate the efficiency and accuracy of the new FFT and CGFFT algorithms. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 29: 47–49, 2001.